1.\" Copyright (c) 1985, 1991 Regents of the University of California. 2.\" All rights reserved. 3.\" 4.\" Redistribution and use in source and binary forms, with or without 5.\" modification, are permitted provided that the following conditions 6.\" are met: 7.\" 1. Redistributions of source code must retain the above copyright 8.\" notice, this list of conditions and the following disclaimer. 9.\" 2. Redistributions in binary form must reproduce the above copyright 10.\" notice, this list of conditions and the following disclaimer in the 11.\" documentation and/or other materials provided with the distribution. 12.\" 3. All advertising materials mentioning features or use of this software 13.\" must display the following acknowledgement: 14.\" This product includes software developed by the University of 15.\" California, Berkeley and its contributors. 16.\" 4. Neither the name of the University nor the names of its contributors 17.\" may be used to endorse or promote products derived from this software 18.\" without specific prior written permission. 19.\" 20.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30.\" SUCH DAMAGE. 31.\" 32.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 33.\" $Id: j0.3,v 1.5 1994/01/11 00:46:54 jtc Exp $ 34.\" 35.Dd April 19, 1991 36.Dt J0 3 37.Os BSD 4 38.Sh NAME 39.Nm j0 , 40.Nm j1 , 41.Nm jn , 42.Nm y0 , 43.Nm y1 , 44.Nm yn 45.Nd bessel functions of first and second kind 46.Sh SYNOPSIS 47.Fd #include <math.h> 48.Ft double 49.Fn j0 "double x" 50.Ft double 51.Fn j1 "double x" 52.Ft double 53.Fn jn "int n" "double x" 54.Ft double 55.Fn y0 "double x" 56.Ft double 57.Fn y1 "double x" 58.Ft double 59.Fn yn "int n" "double x" 60.Sh DESCRIPTION 61The functions 62.Fn j0 63and 64.Fn j1 65compute the 66.Em Bessel function of the first kind of the order 670 and the 68.Em order 691, respectively, 70for the 71real value 72.Fa x ; 73the function 74.Fn jn 75computes the 76.Em Bessel function of the first kind of the integer order 77.Fa n 78for the real value 79.Fa x . 80.Pp 81The functions 82.Fn y0 83and 84.Fn y1 85compute the linearly independent 86.Em Bessel function of the second kind of the order 870 and the 88.Em order 891, respectively, 90for the 91positive 92.Em integer 93value 94.Fa x 95(expressed as a double); 96the function 97.Fn yn 98computes the 99.Em Bessel function of the second kind for the integer order 100.Fa n 101for the positive 102.Em integer 103value 104.Fa x 105(expressed as a double). 106.Sh RETURN VALUES 107If these functions are successful, 108the computed value is returned. On the 109.Tn VAX 110and 111.Tn Tahoe 112architectures, 113a negative 114.Fa x 115value 116results in an error; the global 117variable 118.Va errno 119is set to 120.Er EDOM 121and a reserve operand fault is generated. 122.Sh SEE ALSO 123.Xr math 3 , 124.Xr infnan 3 125.Sh HISTORY 126This set of functions 127appeared in 128.At v7 . 129